Acronym | oho |
TOCID symbol | O|C, aTT |
Name |
octahemioctahedron, facetorectified cube, allelotetratetrahedron |
© © | |
Circumradius | 1 |
Inradius wrt. {3} | +/− sqrt(2/3) = +/− 0.816497 |
Inradius wrt. {6} | 0 |
Vertex figure | [3/2,6,3,6]/0 |
Snub derivation |
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Coordinates | (1/sqrt(2), 1/sqrt(2), 0) & all permutations, all changes of sign |
Volume | 0 |
Surface | 8 sqrt(3) = 13.856406 |
General of army | co |
Colonel of regiment | co |
Volume | 0 |
Surface | 8 sqrt(3) = 13.856406 |
Dihedral angles |
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Face vector | 12, 24, 12 |
Confer |
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External links |
The octahemioctahedron is an edge-faceting of co, in fact it uses the triangles of it and all equatorial hexagons. In fact, the squares of its hull here become pseudo faces only.
When introducing a further vertex at the center and making face intersections into true edges, oho would become an edge-connected shape built from 8 tetrahedra.
This polyhedron could also be understood as a modwrap of that.
Incidence matrix according to Dynkin symbol
x3/2o3x3*a . . . | 12 | 2 2 | 1 2 1 -----------+----+-------+------ x . . | 2 | 12 * | 1 1 0 . . x | 2 | * 12 | 1 0 1 -----------+----+-------+------ x3/2o . | 3 | 3 0 | 4 * * x . x3*a | 6 | 3 3 | * 4 * . o3x | 3 | 0 3 | * * 4 snubbed forms: β3/2o3x3*a, x3/2o3β3*a, β3/2o3β3*a
(isotoxal) 12 | 4 | 2 2 ---+----+---- 2 | 24 | 1 1 ---+----+---- 3 | 3 | 8 * 6 | 6 | * 4
β3o3x both( . . . ) | 12 | 2 2 | 1 1 2 --------------+----+-------+------ both( . . x ) | 2 | 12 * | 0 1 1 sefa( β3o . ) | 2 | * 12 | 1 0 1 --------------+----+-------+------ β3o . ♦ 3 | 0 3 | 4 * * both( . o3x ) | 3 | 3 0 | * 4 * sefa( β3o3x ) | 6 | 3 3 | * * 4 starting figure: x3o3x
β3/2x3x demi( . . . ) | 12 | 2 2 | 2 1 1 ----------------+----+-------+------ both( . x . ) | 2 | 12 * | 1 1 0 both( . . x ) | 2 | * 12 | 1 0 1 ----------------+----+-------+------ both( . x3x ) | 6 | 3 3 | 4 * * β3/2x . ♦ 3 | 3 0 | * 4 * sefa( β3/2x3x ) | 3 | 0 3 | * * 4 starting figure: x3/2x3x
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